Is theoretical physics always computational?

I'm interested a lot in physics and math like most people here and I believe I can say I'm also good at them. I'm also more attracted to theoretical, abstract subjects than experimental or more phenomenological physics. I heard that any "real world" diff eq. more complicated than the hydrogen atom can't be solved analytically so you have to do it with the computer.

Now, the probem is: I don't like programming and find it boring. I'm also not very good at it. Eventually I can write something that works, but it takes a lot of time and effort compared to the result and I have to look up errors on the internet all the time. Are there options to be a theoretical physicist without being good at programming or should I just face it and keep trying to improve my skills?

There are a whole lot of interesting things that can be discovered by doing numerical work, and you shouldn't shy away from getting your hands wet. For example, nearly all results in AdS/CFT are gotten numerically. Also, some programming skills will really help out your job prospects if you don't want to continue in academia for whatever reason (common reasons are not finding a job, and not wanting to be poor well into middle age).

That said, most of what I do is analytical. I do almost all my work by hand, which I have to because programs like Mathematica are incapable of doing it. Getting a result is a long and arduous process. A single sub-calculation could take a week or two. On my current project, I've already written about 150 pages of math, and I'd say I'm about halfway done.